Divisible by this year??? (Part 2: Factorials)

Number Theory Level 3

$n!$ or $n$ -factorial is the product of all integers from $1$ up to $n$ $(n! = 1 \times 2 \times 3 \times ... \times n)$ . Find the maximum integral value of $k$ such that $2014^k$ divides $2014!$

You may also try this problem: Divisible by this year???

This problem is part of the set "Symphony"